Construction of binary matrices for near-optimal compressed sensing

An efficient compressed sensing scheme requires a small number of measurements, a fast recovery algorithm, a small approximation error, and little or no randomness. In 2014, Iwen presented two compressed sensing schemes with near-optimal runtime, based on binary matrices. We combine ideas from these two schemes with a classical construction, used by Porat and Rothschild for near-optimal group testing, to produce a new compressed sensing scheme requiring significantly less randomness without compromising runtime. We give two variants of this compressed sensing scheme: the first is measurement-optimal, and the second is deterministic.

IEEE International Symposium on Information Theory (ISIT) 2021